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Stata Technical Bulletin

STB-57

logit (N=753): Factor Change in Odds
Odds of: inLF vs NotInLF

Ifp I	b	z	P>∣z∣	e^b	e^bStdX	SDofX
kε I	-1.46291	-7.426	0.000	0.2316	0.4646	— 0.5240
k618 I	-0.06457	-0.950	0.342	0.9375	0.9183	1.3199
age I	-0.06287	-4.918	0.000	0.9391	0.6020	8.0726
wc I	0.80727	3.510	0.000	2.2418	1.4381	0.4500
he I	0.11173	0.542	0.588	1.1182	1.0561	0.4885
Iwg I	0.60469	4.009	0.000	1.8307	1.4266	0.5876
inc I	-0.03445	-4.196	0.000	0.9661	0.6698	11.6348
— b = z = P>∣z∣ =	raw coefficient z-score for test of р-value for z-test		b=0			—

e^b = exp(b) = factor change in odds for unit increase in X

e^bStdX = exp(b*SD of X) = change in odds for SD increase in X
SDofX = standard deviation of X

Alternatively, a user might want to interpret the coefficients in terms of their effect on the latent y* that underlies the observed
variable y. Note that to use Iistcoef to compute standardized coefficients does not require that the model be reestimated.

. Iistcoef, std help

logit (N=753): Unstandardized and Standardized Estimates
Observed SD: .49562951
Latent SD: 2.0500391

Odds of: inLF vs NotInLF

— Ifp I	b	z	P>∣z∣	bStdX	bStdY	bStdXY	— SDofX
k5 I	-1.46291	-7.426	0.000	-0.7665	-0.7136	-0.3739	— 0.5240
k618 I	-0.06457	-0.950	0.342	-0.0852	-0.0315	-0.0416	1.3199
age I	-0.06287	-4.918	0.000	-0.5075	-0.0307	-0.2476	8.0726
we I	0.80727	3.510	0.000	0.3633	0.3938	0.1772	0.4500
he I	0.11173	0.542	0.588	0.0546	0.0545	0.0266	0.4885
Iwg I	0.60469	4.009	0.000	0.3553	0.2950	0.1733	0.5876
inc I	-0.03445	-4.196	0.000	-0.4008	-0.0168	-0.1955	11.6348

b = raw coefficient

z = z-score for test of b=0

P>∣z∣ = р-value for z-test

bStdX = х-standardized coefficient
bStdY = у-standardized coefficient

bStdXY = fully standardized coefficient
SDofX = standard deviation of X

Example with mlogit

A key to fully interpreting the multinomial logit model is to consider all contrasts among the outcome categories. The
standard output from mlogit provides contrast between all outcomes and the category specified by basecategory. Here we
specify the rrr option in order to obtain “relative risk ratios” which are also known as factor change coefficients.

. mlogit occ white ed exper, basecategory(1) rrr nolog

Multinomial regression

Log likelihood = -426.80048

Number of obs =
LR chi2(12)

Prob > chi2 =

Pseudo R2 =

337
166.09
0.0000
0.1629

—

occ I

RRR

Std. Err.

P>∣z∣

[957. Conf.

—

Interval]

BlueCol I
white I
ed I
exper I

3.443553
.9053581
1.004732

2.494631
.0926011
.0174807

1.707

-0.972

0.271

0.088

0.331

0.786

.8324658

.7408981

.9710484

—

14.2445

1.106324

1.039585

Craft I

white I
ed I
exper I
---------₊—

1.603748

1.098357

1.028071

.9691607

.1071502

.0171417

0.782

0.962

1.660

0.434

0.336

0.097

.4906218

.9072032

.9950164

—

5.242345

1.329788

1.062223

—

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